© 2017

Progress in Approximation Theory and Applicable Complex Analysis

In Memory of Q.I. Rahman

  • Narendra Kumar Govil
  • Ram Mohapatra
  • Mohammed A. Qazi
  • Gerhard Schmeisser


  • Presents up to date research and advances in approximation theory

  • Bridges classical methods and contemporary approaches to solve problems

  • Contains new insights and serves as a guide to advanced topics


Part of the Springer Optimization and Its Applications book series (SOIA, volume 117)

Table of contents

  1. Front Matter
    Pages i-xxxiv
  2. Geno Nikolov, Alexei Shadrin
    Pages 1-17
  3. Richard Fournier, Stephan Ruscheweyh
    Pages 75-82
  4. Xin Li, Ram Mohapatra, Rajitha Ranasinghe
    Pages 105-127
  5. Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan
    Pages 219-235
  6. Muhammad Aslam Noor, Themistocles M. Rassias, Khalida Inayat Noor, Muhammad Uzair Awan
    Pages 237-268
  7. Yusuf Abu Muhanna, Rosihan M. Ali, Saminathan Ponnusamy
    Pages 269-300
  8. H. N. Mhaskar
    Pages 341-362

About this book


Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics.

The chapters in this book are grouped into four themes; the first,  polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman.


This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.


Approximation Theory Approximation by polynomials Complex Analysis Geometric function theory Inequalities for polynomials Orthogonal polynomials

Editors and affiliations

  • Narendra Kumar Govil
    • 1
  • Ram Mohapatra
    • 2
  • Mohammed A. Qazi
    • 3
  • Gerhard Schmeisser
    • 4
  1. 1.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA
  2. 2.Department of MathematicsUniversity of Central FloridaOrlandoUSA
  3. 3.Department of MathematicsTuskegee UniversityTuskegeeUSA
  4. 4.Department of MathematicsUniversity of Erlangen-NurembergErlangenGermany

Bibliographic information

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